EXAMPLE 7th. Admit a prifm in form of a parallelopipedon as follows; 45.6 inches in length, breadth 27.5 inches, and depth 21.5 inches; what's the content in ale, wine, and malt ? RULE. Multiply the length by the breadth, and that product by the depth, and divide by the fquare divifors. To work the fame by the Slide. Firft find a mean proportional betwixt the Jength and the breadth thus; fet either of the two numbers given upon D to the fame on C, then against the other number on D is the mean requir❜d on C ; D C D C viz. As 27.5: 27.5: 45.6: 35.4 mean length. Then fet each proper gage-point for a fquare to the depth on the lines C and D, and against your mean is the content. As 16.79 21.5: 35.4: Thus As 15.19: 21.5 35.4 : : C 95.6 ale. 116.7 wine. 12.54 malt. Or otherwife you may find the content upon the fide of the Rule A and B ; viz. after finding the area, fet on A to the area on B, then against the depth on A is the content on B. A B B Thus As 282 : 45.6 :: 27.5 : 4.44 | As 231 : 45.6: As 2150: 45.6: 27.5: 5.42 areas. contents. Note. Note. From the foregoing examples it will be obvious how to find the content of any fquare folid or regular prifm with more or lefs fides; viz. to multiply the area of the bafe by the depth and divide by the fquare divifors, &c. Now upon the bottom of the Rule, under the lines A and B, is a reverfe line, mark'd M D, fignifying malt depth; fo that if you fet the length upon M D to the breadth on B, then against the depth on A is the content on B. EXAMPLE. Let the length of a couch be 255 inches, breadth 161, and depth 7.5; what's the content in bushéls ? As 255: 161 :: 7.5: 143.2 Anfwer. EXAMPLE 8th. Suppofe a veffel in form of a cylinder, whofe diameter is 38.7 inches, and the depth 59.5 inches; what's the content in ale, wine, and malt? RULE. Multiply the fquare of the diameter by the depth, and divide by the circular divifors. See the work in the next page. 38.7 The fame by the Slide. Upon the Rule, on the fide D, is the following circular gage-points, (which are the fquare, roots of their proper divifors) viz. 18.94 for ale, 17.14 for wine, and 52.32 for malt. Then fet each proper gage-point on D to the depth on C, and against the diameter on D is the content on C: Thus { D C D C As 18.94 59.5 38.7: 248.2 ale. Thus As 17.14: 59.5: 38.7: 303.1 wine. As 52.32: 59.5: : 38.7: 32.5 malt. EXAMPLE 9th. Admit a tun or veffel, &c. in form of the fruftum of a cone, thus; the greater diameter 40 inches, the leffer diameter 30, and the depth 60 inches; what's the content in ale gallons? RULE. Find the area of each bafe, and a mean proportional between them, multiply the fum of thofe three by one third part of the depth or height, and the product is the content. See the remainder of the work in the next page. |